The invention relates to digital signal processing and specifically to controlling the level of a pulse density modulation (PDM) signal generated by a sigma-delta modulator.
The basic operations of signal processing, multiplication and addition, can be implemented in a known manner by analog signal processing blocks, or an analog signal can be converted into a digital one by using an A/D converter and the desired signal processing operations can be performed digitally. The results can be reconverted into analog signals by using a D/A converter. The A/D and D/A conversions are performed at predetermined sample frequency and at a predetermined resolution.
A/D and D/A convertors based on sigma-delta modulators have become very common recently. In a sigma-delta A/D convertor, a conversion of an analog signal into a baseband digital signal occurs at two stages. At the first stage, an input signal is converted by a sigma-delta modulator into an oversampled single-bit or multibit signal. At the second stage, this oversampled single-bit or multibit signal is decimated to the baseband by using digital filtering. Sigma-delta technique and converters are described for instance in the following articles:
[1] xe2x80x9cAn Overview of Sigma-Delta Convertersxe2x80x9d, P. M. Aziz et al, IEEE Signal Processing Magazine, January 1996, pages 61 to 84.
[2] xe2x80x9cOversampling Delta-sigma Data Converters: Theory, Design and Simulationxe2x80x9d, J. C. Candy et al, IEEE Press NJ 1992, pages 1 to 25.
[3] xe2x80x9cDesign Methodology for Sigma-Delta Modulationxe2x80x9d. B. P. Agrawal et al, IEEE Transactions on Communications, Vol. COM-31, March 1983, pages 360 to 370.
An oversampled output signal of a sigma-delta modulator is a pulse density modulated (PDM) representation of an input signal. In sigma-delta A/D converters, the modulator converts an analog signal into a pulse density modulated (PDM) format. The PDM signal consists of an oversampled single-bit or multibit (e.g. 2 to 4 bits) signal. The relative pulse density of the PDM signal determine represents the amplitude of the input signal. In a frequency domain, the baseband part of the spectrum of the PDM signal is the useful signal band, and at higher frequencies of the spectrum, there is quantization noise produced by a noise processing function of the sigma-delta modulator. It has thus been possible to change the resolution at signal frequencies for over-sampling rate. As known, the noise processing performance of the sigma-delta modulator depends on the order of the modulator, and higher-order modulators remove quantization noise more efficiently from the signal band. By increasing the oversample ratio, the signal band can also be made narrower, in proportion, and the amount of the noise falling on the signal band smaller. Moreover, the amount of noise in the signal band in a sigma-delta modulator can be controlled by the transfer function of the modulator, e.g. by inserting zeroes at suitable frequencies in the transfer function of the modulator.
Solutions for implementing a limited number of signal processing operations by using PDM signals have been presented in the literature lately. The known advantages of digital signal processing are then achieved, such as accuracy, repeatability, unsensitivity to interference, and so on. When a signal is processed directly in an oversampled PDM format, it needs not be converted into a pulse code modulated (PCM) signal at the Nyquist frequency for signal processing. Decimation and interpolation filters generating a baseband PCM signal from a PDM signal can then be omitted in signal processing points. This is a remarkable advantage, because a circuit implementation of a sigma-delta modulator generating the PDM signal is usually small in size and simple, while the decimation and interpolation filter often is a big and complex circuit structure requiring much circuit surface in an integrated circuit implementation and therefore causing additional costs. For instance, the article [4], xe2x80x9cDesign and Analysis of Delta-Sigma Based IIR Filtersxe2x80x9d, D. A. John et al, IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing. Vol. 40, NO. 4, pages 233 to 240, describes an A/D converter having many inputs, each input being filtered separately and summed together before a common decimation filter. An audio mixing board, for instance, can be implemented in this way.
An important form of signal processing is control of signal level: amplification and/or attenuation. This property is very usable especially for audio applications, such as the above-mentioned audio mixing board. Accordingly, it would be preferable, if a PDM signal level also could be controlled. FIG. 1 of the above article [4] shows a sigma-delta attenuator, in which an oversampled 1-bit signal (PDM) is multiplied by a multibit coefficient al and the resulting multibit signal is applied to a digital sigma-delta modulator outputting a 1-bit PDM signal. The multiplier of the 1-bit PDM signal is implemented as a 2-input multiplexor (selector) selecting al or xe2x88x92a1 as an output according to the state of the incoming PDM signal. The article also describes a digital sigma-delta filter suitable for this purpose. The attenuator is possible to implement when said multibit coefficient is lower than one. The feedback value of the sigma-delta modulator being b and said coefficient being a, an attenuation ratio a/b is obtained.
A problem with this known solution is that only an attenuation of a PDM signal has been possible, and therefore, it has been necessary to perform all multiplications by coefficients lower than one. An amplification of a PDM signal has not been considered possible, because the input value of the modulator cannot exceed or even come near the feedback value of the modulator due to the structure of the sigma-delta modulator. The sigma-delta modulator is a conditionally stable structure and the output signals of integrators escape upon the input exceeding a predetermined value. In an analog sigma-delta modulator, the input value is allowed to be normally, depending on the order and the structure of the modulator, approximately 0.3 to 0.7 times the feedback value, cf. article [3]. An amplification of the PDM signal in such a circuit would require an ingoing signal to be multiplied by a number higher than the feedback value. Even if the input level of an A/D modulator were very low and it could, in principle, be amplified quite much by setting the input signal values (a) higher than the feedback value (b), the resulting PDM signal would have only +1 and xe2x88x921 values (single-bit case). By multiplying, the modulator would momentarily obtain too high values. The density and energy of the PDM signal would still be low on an average, but instantaneous values would make the modulator quickly unstable.
An object of the invention is a signal processing method and device, enabling also a relative amplification of a PDM signal, without the noise level increasing remarkably.
The objects of the invention are achieved by a signal processing method comprising the steps of generating an N-bit pulse density modulated signal by a first sigma-delta modulator, where N=1, 2, . . . ; controlling the level of the pulse density modulated signal a) by multiplying the N-bit pulse density modulated signal by a multibit multiplier, the output of which is an M-bit signal, where M greater than N, b) by converting the M-bit signal into an N-but pulse density modulated signal by a digital sigma-delta modulator. The method is according to the invention characterized in that the M-bit signal is converted into the N-bit pulse density modulated signal by the digital sigma-delta modulator having a better signal-to-noise ratio performance than said first sigma-delta modulator.
Another object of the invention is a signal processing system comprising a first sigma-delta modulator generating an N-bit pulse density modulated signal, where N=1, 2, . . . ; means for controlling the level of the pulse density modulated signal, the means comprising a) a multibit multiplier, the input of which is the N-bit pulse density modulated signal and the output an M-bit signal, where M greater than N, b) a digital sigma-delta modulator converting the M-bit signal into the N-bit pulse density modulated signal. The system is according to the invention characterized in that said digital sigma-delta modulator has a better signal-to-noise ratio performance than said first sigma-delta modulator.
A single-bit pulse density modulated PDM signal is generated by the first sigma-delta modulator being an analog modulator, for instance. The level control is performed by multiplying the single-bit PDM signal by a multibit coefficient, so that a multibit stream of numbers is obtained. The number stream is reconverted into a single-bit PDM signal by a second sigma-delta modulator, preferably being a digital modulator.
In accordance with the basic idea of the invention, the signal-to-noise ratio performance of said second sigma-delta modulator, by which the multibit stream of numbers is reconverted into a PDM signal, is better than that of said first sigma-delta modulator. Accordingly, the most significant factor of the total signal-to-noise ratio (SNR) is the noise level of the first sigma-delta modulator, by which the PDM signal originally was generated. In said subsequent second sigma-delta modulator, the PDM signal can be attenuated within a range which is equal to the difference between the SNR performances of the modulators, without any decrease in the total signal-to-noise ratio. For instance, if the SNR of the first sigma-delta modulator is 90 dB at maximum excitation and the SNR of the second sigma-delta modulator is 110 dB, the PDM signal can be attenuated in the second modulator by nearly 20 dB without any decrease in the signal-to-noise ratio. This is possible, because, in the latter modulator, besides the signal, naturally also the noise of the first modulator on the signal band is attenuated and approaches the noise floor set by the second modulator structure.
The PDM signal has thus been scaled to a slightly lower level without any decrease in the performance. Though the second sigma-delta modulator also attenuates the signal, the attenuation may be less than said difference between the performances (20 dB in the above example), whereby a relative amplification is achieved. When the PDM signal is attenuated less than said difference between the SNR performances of the two modulators, the same total signal-to-noise ratio is obtained as by the preceding analog modulator. In the example case, the nominal level of the signal can be fixed to a point where the first modulator gives an unattenuated signal and the second modulator attenuates the signal by 20 dB. The second-order attenuation may be C. In the example case, the total signal-to-noise ratio will then be 90 dB, the signal being between +20-0 dB and 90+20xe2x88x92(c), c being between 20 and 110 dB, and the attenuation of the system thus between 0 and 90 dB.